Is there evidence out there that possibly shows that Matthew and Luke were written first and then Mark followed them? What are some examples?

"Evidence" is a strong term to apply to the Gospels; Biblical scholarship relies on the written books and on tradition, and both literacy and good record-keeping were in short supply in the First Century AD. For this reason, it's believed that the four Gospels were transmitted orally by scholars for 30-70 years before they were actually written down.

Mark, a disciple of St. Paul and someone who never actually met Jesus, is believed to have...

"Evidence" is a strong term to apply to the Gospels; Biblical scholarship relies on the written books and on tradition, and both literacy and good record-keeping were in short supply in the First Century AD. For this reason, it's believed that the four Gospels were transmitted orally by scholars for 30-70 years before they were actually written down.

Mark, a disciple of St. Paul and someone who never actually met Jesus, is believed to have written the first Gospel. It's generally dated to around 65 AD.

Luke is another Gospel writer who is believed to have been a disciple of Paul, not Jesus directly.  His Gospel, as well as Acts of the Apostles, are generally attributed to the same person, whether it was Luke or not. 65-70 AD is the accepted guess.

Matthew, who did know Christ, has a Gospel attributed to him, but it borrows heavily from Mark, which casts serious doubt on its authorship. Biblical scholars date this to 65 - 70 AD , maybe as late as 100 - 134 AD. It’s commonly attributed to a tax collector named Levi.

The Gospel of John was written around 100 AD, but is said to have been approved by him in its oral form. It is so different in tone from the other three that it is not regarded as a “Synoptic” Gospel. Many different Saints John have been conflated into the author of the Gospel according to John.

According to biblical scholar E.P. Sanders, it’s clear that St. Paul never read the Gospels and was apparently unaware of them. Likewise, the Gospel’s authors, including the two whom Paul taught directly, never read his Letters, which implies that they were written after his association with them. But however they were written, Mark and Luke are believed to be the first two, with Matthew a close third.